# Lines resolved by the instrument

1. Dec 29, 2013

### utkarshakash

1. The problem statement, all variables and given/known data
A spectroscopic instrument can resolve two nearby wavelengths λ and λ+Δλ if λ/Δλ is smaller than 8000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument.

3. The attempt at a solution

For Balmer series

$\dfrac{1}{\lambda} = R_H \left( \dfrac{1}{2^2} - \dfrac{1}{n^2} \right)$
1. The problem statement, all variables and given/known data

But what should I substitute for n?

2. Dec 29, 2013

### ehild

n is 3, 4, 5, 6, 7, 8, .....any positive integer >2. You get a wavelength for each n. Find that N so that λ(N)/(λ(N-1)-λ(N))<8000, but λ(N)/(λ(N)-λ(N+1))>8000

ehild

Last edited: Dec 29, 2013
3. Dec 30, 2013

### utkarshakash

I'm facing difficulty finding the n. I tried forming an equation but it is not easy to solve. Hit and trial method does not work for me.

Last edited: Dec 30, 2013
4. Dec 30, 2013

### ehild

You know that the change of a function can be estimated as Δf(x)=(df/dx) Δx.
Your function is λ(n). Take the derivative, and write Δλ/λ as function of n, with Δn=1.

What is the equation you arrive at? It is not easy to solve, you need to estimate. How big can be n? 5? 10? 50? 1000?

Estimation and trial is a method, frequently applied.

ehild